deba@464: /* -*- C++ -*-
deba@464:  *
deba@464:  * This file is a part of LEMON, a generic C++ optimization library
deba@464:  *
deba@464:  * Copyright (C) 2003-2008
deba@464:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
deba@464:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
deba@464:  *
deba@464:  * Permission to use, modify and distribute this software is granted
deba@464:  * provided that this copyright notice appears in all copies. For
deba@464:  * precise terms see the accompanying LICENSE file.
deba@464:  *
deba@464:  * This software is provided "AS IS" with no warranty of any kind,
deba@464:  * express or implied, and with no claim as to its suitability for any
deba@464:  * purpose.
deba@464:  *
deba@464:  */
deba@464: 
deba@464: #ifndef RADIX_SORT_H
deba@464: #define RADIX_SORT_H
deba@464: 
deba@464: /// \ingroup auxalg
deba@464: /// \file
deba@464: /// \brief Radix sort
deba@464: ///
deba@464: /// Linear time sorting algorithms
deba@464: 
deba@464: #include <vector>
deba@464: #include <limits>
deba@464: #include <iterator>
deba@464: #include <algorithm>
deba@464: 
deba@464: namespace lemon {
deba@464: 
deba@464:   namespace _radix_sort_bits {
deba@464: 
deba@464:     template <typename Value>
deba@464:     struct Identity {
deba@464:       const Value& operator()(const Value& val) {
deba@464: 	return val;
deba@464:       }
deba@464:     };
deba@464: 
deba@464: 
deba@464:     template <typename Value, typename Iterator, typename Functor>
deba@464:     Iterator radixSortPartition(Iterator first, Iterator last, 
deba@464: 				Functor functor, Value mask) {
deba@464:       while (first != last && !(functor(*first) & mask)) {
deba@464: 	++first;
deba@464:       }
deba@464:       if (first == last) {
deba@464: 	return first;
deba@464:       }
deba@464:       --last;
deba@464:       while (first != last && (functor(*last) & mask)) {
deba@464: 	--last;
deba@464:       }
deba@464:       if (first == last) {
deba@464: 	return first;
deba@464:       }
deba@464:       std::iter_swap(first, last);
deba@464:       ++first;
deba@464:       if (!(first < last)) {
deba@464: 	return first;
deba@464:       }
deba@464:       while (true) {
deba@464: 	while (!(functor(*first) & mask)) {
deba@464: 	  ++first;
deba@464: 	}
deba@464: 	--last;
deba@464: 	while (functor(*last) & mask) {
deba@464: 	  --last;
deba@464: 	}
deba@464: 	if (!(first < last)) {
deba@464: 	  return first;
deba@464: 	}
deba@464: 	std::iter_swap(first, last);
deba@464: 	++first;
deba@464:       }
deba@464:     }
deba@464: 
deba@464:     template <typename Iterator, typename Functor>
deba@464:     Iterator radixSortSignPartition(Iterator first, Iterator last, 
deba@464: 				    Functor functor) {
deba@464:       while (first != last && functor(*first) < 0) {
deba@464: 	++first;
deba@464:       }
deba@464:       if (first == last) {
deba@464: 	return first;
deba@464:       }
deba@464:       --last;
deba@464:       while (first != last && functor(*last) >= 0) {
deba@464: 	--last;
deba@464:       }
deba@464:       if (first == last) {
deba@464: 	return first;
deba@464:       }
deba@464:       std::iter_swap(first, last);
deba@464:       ++first;
deba@464:       if (!(first < last)) {
deba@464: 	return first;
deba@464:       }
deba@464:       while (true) {
deba@464: 	while (functor(*first) < 0) {
deba@464: 	  ++first;
deba@464: 	}
deba@464: 	--last;
deba@464: 	while (functor(*last) >= 0) {
deba@464: 	  --last;
deba@464: 	}
deba@464: 	if (!(first < last)) {
deba@464: 	  return first;
deba@464: 	}
deba@464: 	std::iter_swap(first, last);
deba@464: 	++first;
deba@464:       }
deba@464:     }
deba@464: 
deba@464:     template <typename Value, typename Iterator, typename Functor>
deba@464:     void radixIntroSort(Iterator first, Iterator last, 
deba@464: 			Functor functor, Value mask) {
deba@464:       while (mask != 0 && last - first > 1) {
deba@464: 	Iterator cut = radixSortPartition(first, last, functor, mask);
deba@464: 	mask >>= 1;
deba@464: 	radixIntroSort(first, cut, functor, mask);
deba@464: 	first = cut;
deba@464:       }
deba@464:     }
deba@464: 
deba@464:     template <typename Value, typename Iterator, typename Functor>
deba@464:     void radixSignedSort(Iterator first, Iterator last, Functor functor) {
deba@464: 
deba@464:       Iterator cut = radixSortSignPartition(first, last, functor);
deba@464: 
deba@464:       Value mask;
deba@464:       int max_digit;
deba@464:       Iterator it;
deba@464: 
deba@464:       mask = ~0; max_digit = 0;
deba@464:       for (it = first; it != cut; ++it) {
deba@464: 	while ((mask & functor(*it)) != mask) {
deba@464: 	  ++max_digit;
deba@464: 	  mask <<= 1;
deba@464: 	}
deba@464:       }
deba@464:       radixIntroSort(first, cut, functor, 1 << max_digit);
deba@464: 
deba@464:       mask = 0; max_digit = 0;
deba@464:       for (it = cut; it != last; ++it) {
deba@464: 	while ((mask | functor(*it)) != mask) {
deba@464: 	  ++max_digit;
deba@464: 	  mask <<= 1; mask |= 1;
deba@464: 	}
deba@464:       }
deba@464:       radixIntroSort(cut, last, functor, 1 << max_digit);
deba@464:     }
deba@464: 
deba@464:     template <typename Value, typename Iterator, typename Functor>
deba@464:     void radixUnsignedSort(Iterator first, Iterator last, Functor functor) {
deba@464: 
deba@464:       Value mask = 0;
deba@464:       int max_digit = 0;
deba@464: 
deba@464:       Iterator it;
deba@464:       for (it = first; it != last; ++it) {
deba@464: 	while ((mask | functor(*it)) != mask) {
deba@464: 	  ++max_digit;
deba@464: 	  mask <<= 1; mask |= 1;
deba@464: 	}
deba@464:       }
deba@464:       radixIntroSort(first, last, functor, 1 << max_digit);
deba@464:     }
deba@464: 
deba@464: 
deba@464:     template <typename Value, 
deba@464: 	      bool sign = std::numeric_limits<Value>::is_signed >
deba@464:     struct RadixSortSelector {
deba@464:       template <typename Iterator, typename Functor>
deba@464:       static void sort(Iterator first, Iterator last, Functor functor) {
deba@464: 	radixSignedSort<Value>(first, last, functor);
deba@464:       }
deba@464:     };
deba@464: 
deba@464:     template <typename Value>
deba@464:     struct RadixSortSelector<Value, false> {
deba@464:       template <typename Iterator, typename Functor>
deba@464:       static void sort(Iterator first, Iterator last, Functor functor) {
deba@464: 	radixUnsignedSort<Value>(first, last, functor);
deba@464:       }
deba@464:     };
deba@464: 
deba@464:   }
deba@464: 
deba@464:   /// \ingroup auxalg
deba@464:   ///
deba@464:   /// \brief Sorts the STL compatible range into ascending order.
deba@464:   ///
deba@464:   /// The \c radixSort sorts the STL compatible range into ascending
deba@464:   /// order.  The radix sort algorithm can sort the items which mapped
deba@464:   /// to an integer with an adaptable unary function \c functor and the
deba@464:   /// order will be ascending by these mapped values. As function
deba@464:   /// specialization it is possible to use a normal function instead
deba@464:   /// of the functor object or if the functor is not given it will use
deba@464:   /// an identity function instead.
deba@464:   ///
deba@464:   /// This implemented radix sort is a special quick sort which pivot
deba@464:   /// value is choosen to partite the items on the next
deba@464:   /// bit. Therefore, let be \c c the maximal capacity and \c n the
deba@464:   /// number of the items in the container, the time complexity of the
deba@464:   /// algorithm is \f$ O(\log(c)n) \f$ and the additional space
deba@464:   /// complexity is \f$ O(\log(c)) \f$.
deba@464:   ///
deba@464:   /// \param first The begin of the given range.
deba@464:   /// \param last The end of the given range.
deba@464:   /// \param functor An adaptible unary function or a normal function
deba@464:   /// which maps the items to any integer type which can be either
deba@464:   /// signed or unsigned.
deba@464:   template <typename Iterator, typename Functor>
deba@464:   void radixSort(Iterator first, Iterator last, Functor functor) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     typedef typename Functor::result_type Value;
deba@464:     RadixSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator, typename Value, typename Key>
deba@464:   void radixSort(Iterator first, Iterator last, Value (*functor)(Key)) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     RadixSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator, typename Value, typename Key>
deba@464:   void radixSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     RadixSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator, typename Value, typename Key>
deba@464:   void radixSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     RadixSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator, typename Value, typename Key>
deba@464:   void radixSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     RadixSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator>
deba@464:   void radixSort(Iterator first, Iterator last) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     typedef typename std::iterator_traits<Iterator>::value_type Value;
deba@464:     RadixSortSelector<Value>::sort(first, last, Identity<Value>());
deba@464:   }
deba@464: 
deba@464:   namespace _radix_sort_bits {
deba@464: 
deba@464:     template <typename Value>
deba@464:     unsigned char valueByte(Value value, int byte) {
deba@464:       return value >> (std::numeric_limits<unsigned char>::digits * byte);
deba@464:     }
deba@464: 
deba@464:     template <typename Functor, typename Key>
deba@464:     void counterIntroSort(Key *first, Key *last, Key *target, 
deba@464: 			  int byte, Functor functor) {
deba@464:       const int size = 
deba@464: 	unsigned(std::numeric_limits<unsigned char>::max()) + 1;
deba@464:       std::vector<int> counter(size);
deba@464:       for (int i = 0; i < size; ++i) {
deba@464: 	counter[i] = 0;
deba@464:       }
deba@464:       Key *it = first;
deba@464:       while (first != last) {
deba@464: 	++counter[valueByte(functor(*first), byte)]; 
deba@464: 	++first;
deba@464:       }
deba@464:       int prev, num = 0;
deba@464:       for (int i = 0; i < size; ++i) {
deba@464: 	prev = num;
deba@464: 	num += counter[i];
deba@464: 	counter[i] = prev;
deba@464:       }
deba@464:       while (it != last) {
deba@464: 	target[counter[valueByte(functor(*it), byte)]++] = *it;
deba@464: 	++it;
deba@464:       }
deba@464:     }
deba@464: 
deba@464:     template <typename Functor, typename Key>
deba@464:     void signedCounterIntroSort(Key *first, Key *last, Key *target, 
deba@464: 				int byte, Functor functor) {
deba@464:       const int size = 
deba@464: 	unsigned(std::numeric_limits<unsigned char>::max()) + 1;
deba@464:       std::vector<int> counter(size);
deba@464:       for (int i = 0; i < size; ++i) {
deba@464: 	counter[i] = 0;
deba@464:       }
deba@464:       Key *it = first;
deba@464:       while (first != last) {
deba@464: 	counter[valueByte(functor(*first), byte)]++;
deba@464: 	++first;
deba@464:       }
deba@464:       int prev, num = 0;
deba@464:       for (int i = size / 2; i < size; ++i) {
deba@464: 	prev = num;
deba@464: 	num += counter[i];
deba@464: 	counter[i] = prev;
deba@464:       }
deba@464:       for (int i = 0; i < size / 2; ++i) {
deba@464: 	prev = num;
deba@464: 	num += counter[i];
deba@464: 	counter[i] = prev;
deba@464:       }
deba@464:       while (it != last) {
deba@464: 	target[counter[valueByte(functor(*it), byte)]++] = *it;
deba@464: 	++it;
deba@464:       }
deba@464:     }
deba@464: 
deba@464:   
deba@464:     template <typename Value, typename Iterator, typename Functor>
deba@464:     void counterSignedSort(Iterator first, Iterator last, Functor functor) {
deba@464:       if (first == last) return;
deba@464:       typedef typename std::iterator_traits<Iterator>::value_type Key;
deba@464:       typedef std::allocator<Key> Allocator;
deba@464:       Allocator allocator;
deba@464: 
deba@464:       int length = std::distance(first, last);
deba@464:       Key* buffer = allocator.allocate(2 * length);
deba@464:       try {
deba@464: 	bool dir = true;
deba@464: 	std::copy(first, last, buffer);
deba@464: 	for (int i = 0; i < int(sizeof(Value)) - 1; ++i) {
deba@464: 	  if (dir) {
deba@464: 	    counterIntroSort(buffer, buffer + length, buffer + length, 
deba@464: 			     i, functor);
deba@464: 	  } else {
deba@464: 	    counterIntroSort(buffer + length, buffer + 2 * length, buffer, 
deba@464: 			     i, functor);
deba@464: 	  }
deba@464: 	  dir = !dir;
deba@464: 	}
deba@464: 	if (dir) {
deba@464: 	  signedCounterIntroSort(buffer, buffer + length, buffer + length, 
deba@464: 				 sizeof(Value) - 1, functor);
deba@464: 	  std::copy(buffer + length, buffer + 2 * length, first);
deba@464: 	}	else {
deba@464: 	  signedCounterIntroSort(buffer + length, buffer + 2 * length, buffer, 
deba@464: 				 sizeof(Value) - 1, functor);
deba@464: 	  std::copy(buffer, buffer + length, first);
deba@464: 	}
deba@464:       } catch (...) {
deba@464: 	allocator.deallocate(buffer, 2 * length);
deba@464: 	throw;
deba@464:       }
deba@464:       allocator.deallocate(buffer, 2 * length);
deba@464:     }
deba@464: 
deba@464:     template <typename Value, typename Iterator, typename Functor>
deba@464:     void counterUnsignedSort(Iterator first, Iterator last, Functor functor) {
deba@464:       if (first == last) return;
deba@464:       typedef typename std::iterator_traits<Iterator>::value_type Key;
deba@464:       typedef std::allocator<Key> Allocator;
deba@464:       Allocator allocator;
deba@464: 
deba@464:       int length = std::distance(first, last);
deba@464:       Key *buffer = allocator.allocate(2 * length);
deba@464:       try {
deba@464: 	bool dir = true;
deba@464: 	std::copy(first, last, buffer);
deba@464: 	for (int i = 0; i < int(sizeof(Value)); ++i) {
deba@464: 	  if (dir) {
deba@464: 	    counterIntroSort(buffer, buffer + length, 
deba@464: 			     buffer + length, i, functor);
deba@464: 	  } else {
deba@464: 	    counterIntroSort(buffer + length, buffer + 2 * length, 
deba@464: 			     buffer, i, functor);
deba@464: 	  }
deba@464: 	  dir = !dir;
deba@464: 	}
deba@464: 	if (dir) {
deba@464: 	  std::copy(buffer, buffer + length, first);
deba@464: 	}	else {
deba@464: 	  std::copy(buffer + length, buffer + 2 * length, first);
deba@464: 	}
deba@464:       } catch (...) {
deba@464: 	allocator.deallocate(buffer, 2 * length);
deba@464: 	throw;
deba@464:       }
deba@464:       allocator.deallocate(buffer, 2 * length);
deba@464:     }
deba@464: 
deba@464: 
deba@464: 
deba@464:     template <typename Value, 
deba@464: 	      bool sign = std::numeric_limits<Value>::is_signed >
deba@464:     struct CounterSortSelector {
deba@464:       template <typename Iterator, typename Functor>
deba@464:       static void sort(Iterator first, Iterator last, Functor functor) {
deba@464: 	counterSignedSort<Value>(first, last, functor);
deba@464:       }
deba@464:     };
deba@464: 
deba@464:     template <typename Value>
deba@464:     struct CounterSortSelector<Value, false> {
deba@464:       template <typename Iterator, typename Functor>
deba@464:       static void sort(Iterator first, Iterator last, Functor functor) {
deba@464: 	counterUnsignedSort<Value>(first, last, functor);
deba@464:       }
deba@464:     };
deba@464: 
deba@464:   }
deba@464: 
deba@464:   /// \ingroup auxalg
deba@464:   ///
deba@464:   /// \brief Sorts stable the STL compatible range into ascending order.
deba@464:   ///
deba@464:   /// The \c counterSort sorts the STL compatible range into ascending
deba@464:   /// order.  The counter sort algorithm can sort the items which
deba@464:   /// mapped to an integer with an adaptable unary function \c functor
deba@464:   /// and the order will be ascending by these mapped values. As
deba@464:   /// function specialization it is possible to use a normal function
deba@464:   /// instead of the functor object or if the functor is not given it
deba@464:   /// will use an identity function instead.
deba@464:   ///
deba@464:   /// The implemented counter sort use a radix forward sort on the
deba@464:   /// bytes of the integer number. The algorithm sorts the items
deba@464:   /// byte-by-byte, first it counts how many times occurs a byte value
deba@464:   /// in the containerm, and with the occurence number the container
deba@464:   /// can be copied to an other in asceding order in \c O(n) time.
deba@464:   /// Let be \c c the maximal capacity of the integer type and \c n
deba@464:   /// the number of the items in the container, the time complexity of
deba@464:   /// the algorithm is \f$ O(\log(c)n) \f$ and the additional space
deba@464:   /// complexity is \f$ O(n) \f$.
deba@464:   ///
deba@464:   /// The sorting algorithm is stable, i.e. the order of two equal
deba@464:   /// element remains the same.
deba@464:   ///
deba@464:   /// \param first The begin of the given range.
deba@464:   /// \param last The end of the given range.
deba@464:   /// \param functor An adaptible unary function or a normal function
deba@464:   /// which maps the items to any integer type which can be either
deba@464:   /// signed or unsigned.
deba@464:   template <typename Iterator, typename Functor>
deba@464:   void counterSort(Iterator first, Iterator last, Functor functor) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     typedef typename Functor::result_type Value;
deba@464:     CounterSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator, typename Value, typename Key>
deba@464:   void counterSort(Iterator first, Iterator last, Value (*functor)(Key)) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     CounterSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator, typename Value, typename Key>
deba@464:   void counterSort(Iterator first, Iterator last, Value& (*functor)(Key)) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     CounterSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator, typename Value, typename Key>
deba@464:   void counterSort(Iterator first, Iterator last, Value (*functor)(Key&)) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     CounterSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator, typename Value, typename Key>
deba@464:   void counterSort(Iterator first, Iterator last, Value& (*functor)(Key&)) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     CounterSortSelector<Value>::sort(first, last, functor);
deba@464:   }
deba@464: 
deba@464:   template <typename Iterator>
deba@464:   void counterSort(Iterator first, Iterator last) {
deba@464:     using namespace _radix_sort_bits;
deba@464:     typedef typename std::iterator_traits<Iterator>::value_type Value;
deba@464:     CounterSortSelector<Value>::sort(first, last, Identity<Value>());
deba@464:   }
deba@464: 
deba@464: }
deba@464: 
deba@464: #endif